According to the PMBOK® Guide (Project Management Body of Knowledge), specifically the Project Schedule Management knowledge area and the Critical Path Method (CPM), we must calculate the duration of every possible path from " Start " to " End " to distinguish between the critical and non-critical paths.

Based on the network diagram provided in the previous sequence (Questions 163-164):

Analyze all Network Paths:

Path 1: A (1) → B (4) → C (6) → F (5) → G (7) → I (2) = 25 days (Critical Path)

Path 2: A (1) → B (4) → C (6) → F (5) → H (3) → I (2) = 21 days (Non-critical)

Path 3: A (1) → D (2) → E (3) → F (5) → G (7) → I (2) = 20 days (Non-critical)

Path 4: A (1) → D (2) → E (3) → F (5) → H (3) → I (2) = 16 days (Non-critical)

Identify the Shortest Non-Critical Path:

The Critical Path is the longest path (25 days).

Any path with a duration less than the Critical Path is a Non-Critical Path.

Comparing the non-critical durations (21, 20, and 16), the path with the minimum value is Path 4, which totals 16 days.

In the PMI framework, identifying the shortest path helps the Project Manager understand which sequences of activities have the most Total Float. In this specific network, the path A-D-E-F-H-I has the most flexibility, with a total float of $25 - 16 = 9$ days.